Profit & Loss Extra Questions And Answers - Class 5 Mathematics | Quick Revision Study Guide

Q1: An article is purchased for Rs. 450 and sold for Rs. 500. Find the gain percent.
Ans:
Gain = SP - CP = 500 - 450 = 50.
Gain% = (Gain/CP) × 100 = (50/450) × 100 = 100/9 % ≈ 11.11%.

Q2: A man sold a fan for Rs. 465. Find the cost price if he incurred a loss of 7%.
Ans:
Loss% = 7% so SP = 93% of CP.
CP = (100/93) × SP = (100/93) × 465 = 500.
Therefore, the cost price of the fan = Rs. 500.

Q3: In a transaction, the profit percentage is 80% of the cost. If the cost further increases by 20% but the selling price remains the same, how much is the decrease in profit percentage?
Ans:
Assume CP = Rs. 100.
Profit = 80% of 100 = Rs. 80, so SP = CP + Profit = 100 + 80 = Rs. 180.
If cost increases by 20% → New CP = 120.
New profit = SP - New CP = 180 - 120 = Rs. 60.
New profit% = (60/120) × 100 = 50%.
Decrease in profit percentage = 80% - 50% = 30 percentage points.

 Q4: A man bought some toys at the rate of 10 for Rs. 40 and sold them at 8 for Rs. 35. Find his gain or loss per cent.
Ans:
Cost price of 10 toys = Rs. 40 → CP of 1 toy = Rs. 40/10 = Rs. 4.
Selling price of 8 toys = Rs. 35 → SP of 1 toy = 35/8 = Rs. 4.375.
Gain per toy = SP - CP = 4.375 - 4 = 0.375 = 3/8.
Gain% = (Gain/CP) × 100 = (0.375/4) × 100 = 9.375%.

Q5: The cost price of 10 pens is the same as the selling price of n pens. If there is a loss of 40%, approximately what is the value of n?
Ans:
Let CP per pen = c and SP per pen = s.
Given: CP of 10 pens = SP of n pens → 10c = n s.
Loss 40% means s = 60% of c = 0.6c.
So 10c = n × 0.6c → 10 = 0.6 n → n = 10/0.6 = 100/6 ≈ 16.67 ≈ 17.

Q6: A dishonest merchant sells his grocery using weights 15% less than the true weights and makes a profit of 20%. Find his total gain percentage.
Ans:
Let the cost price of 1 kg = Rs. 100 (assume for easy calculation).
Marked selling price for 1 kg with 20% profit = 120% of 100 = Rs. 120.
But using weights 15% less, when he sells "1 kg" he actually gives only 85% of 1 kg = 0.85 kg.
Cost of the 0.85 kg he gives = 0.85 × 100 = Rs. 85.
Profit on that sale = SP - actual cost = 120 - 85 = Rs. 35.
Total gain% = (Profit / Actual cost) × 100 = (35/85) × 100 ≈ 41.176% ≈ 41.18%.

Q 7: A man bought two bicycles for Rs. 2500 each. If he sells one at a profit of 5%, then how much should he sell the other so that he makes a profit of 20% on the whole?
Ans:
Total cost for two = 2500 + 2500 = Rs. 5000.
Required total selling price for 20% overall profit = 120% of 5000 = Rs. 6000.
He sells one at 5% profit → SP₁ = 105% of 2500 = 1.05 × 2500 = Rs. 2625.
Required SP for the other bike = 6000 - 2625 = Rs. 3375.
Profit% on the second bike = [(3375 - 2500)/2500] × 100 = (875/2500) × 100 = 35%.

Q8: A shopkeeper allows a discount of 10% on the marked price and still gains 17% on the whole. Find at what per cent above the cost price did he mark his goods.
Ans:
Let CP = Rs. 100.
Since he gains 17%, SP = Rs. 117.
SP = 90% of marked price (after 10% discount) → 0.9 × Marked price = 117.
Marked price = 117 / 0.9 = 130.
Marked above cost = (130 - 100)/100 × 100 = 30%.

Q 9: A shopkeeper offers a discount of 20% on the selling price. On a special sale day, he offers an extra 25% off coupon after the first discount. If the article was sold for Rs. 3600, find

1. The marked price of the article and
2. The cost price if the shopkeeper still makes a profit of 80% on the whole after all discounts are applied.

Ans:
Let the marked price be x.
After the first discount of 20%, the price becomes 80% of x. After an extra 25% off, the final price = 75% of that.
So final price = 75% of 80% of x = 0.75 × 0.8 × x = 0.6 x = 3600 → x = 3600/0.6 = 6000.
Thus, marked price = Rs. 6000.
If final SP = Rs. 3600 and this gives an overall profit of 80%, then SP = 180% of CP → CP = SP/1.8 = 3600/1.8 = Rs. 2000.

Q10: A person buys 60 oranges at the rate of  Rs. 21 per dozen and sells them at the rate of  Rs.24 per dozen.
Ans: CP of 1 dozen oranges = 21.
Number of dozens in 60 oranges = 60/12 = 5 dozen.
CP of 60 oranges = 21 × 5 = Rs. 105.
SP of 1 dozen = 24 → SP of 5 dozen = 24 × 5 = Rs. 120.
Profit = SP - CP = 120 - 105 = Rs. 15.